Proportional Recovery After Stroke: Addressing Concerns Regarding Mathematical Coupling and Ceiling Effects

Abstract

Baseline scores after stroke have long been known as a good predictor of post-stroke outcomes. Similarly, the extent of baseline impairment has been shown to strongly correlate with spontaneous recovery in the first 3 to 6 months after stroke, a principle known as proportional recovery. However, recent critiques have proposed that proportional recovery is confounded, most notably by mathematical coupling and ceiling effects, and that it may not be a valid model for post-stroke recovery. This article reviews the current understanding of proportional recovery after stroke, discusses its supposed confounds of mathematical coupling and ceiling effects, and comments on the validity and usefulness of proportional recovery as a model for post-stroke recovery. We demonstrate that mathematical coupling of the true measurement value is not a real statistical confound, but rather a notational construct that has no effect on the correlation itself. On the other hand, mathematical coupling does apply to the measurement error and can spuriously amplify correlation effect sizes, but should be negligible in most cases. We also explain that compression toward ceiling and the corresponding proportional recovery relationship are consistent with our understanding of post-stroke recovery dynamics, rather than being unwanted confounds. However, while proportional recovery is valid, it is not particularly groundbreaking or meaningful as previously thought, just like how correlations between baseline scores and outcomes are relatively common in stroke research. Whether through proportional recovery or baseline-outcome regression, baseline scores are a starting point for investigating factors that determine recovery and outcomes after stroke.

Aphasia improvement without logotherapy during motor neurorehabilitation of post-stroke hemiparesis using virtual reality or modified constraint-induced movement therapy: A retrospective cohort

“…Although the post-stroke clinical evolution could be moderately influenced by some clinical factors, such as sex, age, time of evolution, and location or size of the infarct, especially during the first 3 to 6 months ( Prabhakaran et al, 2008 ), spontaneous recovery or “proportional recovery” in this period, it has currently been questioned as a valid recovery model after EVC due to possible mathematical coupling errors and ceiling effects. However, it is still considered useful ( Chong et al, 2023 ) and the measurement of clinical predictors in various studies would be important. Although it was not part of the objective of this work, its measurement could be considered in the following investigations.…”